Is it permissible for a widow to marry her deceased husband's brother, knowing that he is five years younger than her and has not yet completed military service, given the pressures from his family and her desire to stay and serve her mother-in-law?

There is no harm in marrying the brother of the deceased husband if he is a man of religion and good character. In fact, he would be the most preferable choice for several reasons, including: 1. Responding to the command of Islamic law to marry a person of religion and good character. 2. It is expected that he will show kindness and affection towards your daughter, as he is her paternal uncle. 3. Your daughter will remain under your custody. 4. Gaining the affection of your daughter's family.

As for him being younger in age, it has no effect, for how many women have married men younger than them and found happiness in their marital lives.